But there are certainly other words or phrases in one language which require more circumlocution in another language. Most obvious are animal or plant names where the animal or plant does not exist in the home lands of both languages--there is no single word for 'narwhal' in Tzeltal, and there is no word in English (outside of the scientific name) for many plants familiar to the Tzeltales.
Less obviously, there are words in one language for concepts that you can certainly wrap your mind around in another language, but for which there's no one-word or even standard phrasal translation in another. I heard a commercial in Spanish for some company on the radio, which ended with the single word sentence "Cumplimos!" It was obvious to me as a second language learner of Spanish what this meant (something like "we finish what we promise you we'll do"), but I could not come up with a simple translation (the literal translation "We complete" does not hack it).
There are a lot of words for concrete things, like the example you gave. But also specific words for abstractions.
I suspect, for instance, that Korean has a word for communism which has that one specific meaning.
I think the article is not so much getting at the unfamiliar plant names or cultural things like names of foods.
But for instance verbs. In English you can take a nap, take a wife, take a stand, take a leak, take someone somewhere, take the money and run, ... In another language, you need different verbs for these. But some of those verbs in that language also have multiple meanings. If we pin down the specific usage frame, like "take a nap", there is a specific translation that fits. This doesn't involve geographic or cultural items; everyone everywhere takes naps.
Verbs are often like this because they involve metaphor a lot.
Nouns also involve metaphor, often when some less common objects are named after common ones. E.g. mouth is a body part. Skirt and sleeve are parts of clothing. A river can have a mouth in English; maybe it would be funny in another language. Technical objects can have skirts (protective guards) or sleeves (sliding casings). Maybe in the foreign language you cannot use those clothing words for those objects without sounding funny.
"We follow through" could work for cumplimos. I suspect that it may be a word that is used often in ads? So in the translation you have to lose exactness and map hackneyed to hackneyed, same sort of thing to the same sort of thing. E.g. "we go the distance" or whatever.
That generalization is completely false. There are situations where that is the case, and situations where there is an exact correspondence between words that have the same meaning or set of meanings.
Even when there isn't a correspondence, context usually resolves it. The word pairs have overlapping meanings and there is a situation in which that overlap applies, and so they are an exact translation.